Changing Physics of Waving Flag in Python
I already figured this out myself. It seems like the following order of calls is successful. The trick is to perform a free_bake and then calling bake_all after changing the physics parameters:

bpy.ops.ptcache.free_bake_all()

# Increase the wind speed (default: 1000)
bpy.data.objects['Field'].field.strength = 0.0

# And bake the new simulation...
bpy.ops.ptcache.bake_all(bake=True)